DESCRIPTION (Applicant's Description) Disease-incidence or disease-mortality data are often reported for small areas and displayed using a choropleth map, e.g., in cancer atlases. Areas with extremely high incidence rates may be subject to further scrutiny in an attempt to identify possible risk factors. Case-control studies may then be carried out to estimate the effects of a particular risk factor. This research program is intended to explore, over the long term, a number of statistical issues related to the display, analysis, and interpretation of disease-incidence or disease-mortality data. The specific aims of this small grant application include improved small-area estimation with a focus on identifying regions with extreme rates, and identification of the regions, if any, that exhibit rates beyond what might be expected due to chance fluctuations. It is expected that this research will lead into building point-level epidemiological mechanisms into a model for small-area data, and the visualization of data and results using a Geographic Information System. The primary research tool for the goals of this application is a Bayesian hierarchical model for small-area disease incidence data. Three approaches to inference for extreme values are to be investigated: inference directly from the posterior distribution of small-area disease rates, constrained Bayesian estimation using squared-error loss, and Bayesian estimation based on loss functions emphasizing extrema.